Block #604,894

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/28/2014, 3:28:27 AM · Difficulty 10.9099 · 6,196,435 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
a133759de2b6f0738e8ec6a40223bed8e47bf5cd584bae1f99d0a1494b71dae7

Height

#604,894

Difficulty

10.909900

Transactions

5

Size

1.20 KB

Version

2

Bits

0ae8ef3d

Nonce

1,330,333,293

Timestamp

6/28/2014, 3:28:27 AM

Confirmations

6,196,435

Merkle Root

a02704cc32a605199429b8fafa94b04b48bb687af15fb4bcc99e0ef49e7ef6ea
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.892 × 10⁹⁹(100-digit number)
18929412480756885422…57553634388620267521
Discovered Prime Numbers
p_k = 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
1.892 × 10⁹⁹(100-digit number)
18929412480756885422…57553634388620267521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.785 × 10⁹⁹(100-digit number)
37858824961513770844…15107268777240535041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.571 × 10⁹⁹(100-digit number)
75717649923027541689…30214537554481070081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.514 × 10¹⁰⁰(101-digit number)
15143529984605508337…60429075108962140161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.028 × 10¹⁰⁰(101-digit number)
30287059969211016675…20858150217924280321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.057 × 10¹⁰⁰(101-digit number)
60574119938422033351…41716300435848560641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.211 × 10¹⁰¹(102-digit number)
12114823987684406670…83432600871697121281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.422 × 10¹⁰¹(102-digit number)
24229647975368813340…66865201743394242561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.845 × 10¹⁰¹(102-digit number)
48459295950737626681…33730403486788485121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.691 × 10¹⁰¹(102-digit number)
96918591901475253362…67460806973576970241
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,654,701 XPM·at block #6,801,328 · updates every 60s
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